Dr Pavel Gapeev

This course is available on the BSc in Actuarial Science, BSc in Mathematics and Economics, BSc in Mathematics with Data Science, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

Mathematical Methods (MA100) and Introduction to Abstract Mathematics (MA103) (or MA102) are pre-requisites. Real Analysis (MA203) and/or Further Mathematical Methods (MA212) are highly desirable, and students who have done neither MA203 nor MA212 should contact the lecturer.

The course concentrates on the theory and qualitative analysis of (ordinary) differential equations, although some solution techniques will be considered as well. Special attention will be paid to geometric concepts and the role of differential equations in the theory of dynamical systems. Specific topics covered are: First examples; illustrations of use of the computer package Maple. Existence and uniqueness of solutions. Autonomous 1 and 2 dimensional systems. Linear equations and systems: phase portraits; classification of systems in the plane; higher dimensional systems and higher order equations. Nonlinear systems in the plane: local and global behaviour; linearisation and stability at equilibrium points; Lyapunov functions; limit cycles. Control theory; linear systems; controllability.

This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours across Winter Term.

Written answers to set problems will be expected on a weekly basis.

Full notes will be handed out throughout the course. A good additional text book is D K Arrowsmith & C M Place, Dynamical Systems - Differential Equations, Maps and Chaotic Behaviour. Other books closely related to R Grimshaw, Nonlinear Ordinary Differential Equations and W A Brock & A G Malliaris, Differential Equations, Stability and Chaos in Dynamic Economics.

Exam (100%, duration: 2 hours) in the spring exam period.